CAPT OF LGT ACFT DEVIATED FROM ASSIGNED COURSE AND ALT DUE TO THE ACFT'S INTERMITTENT XMITTER MIKE.

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I FLEW FLT FROM DAYTONA BEACH TO RALEIGH DURHAM. I WAS ASKED TO CALL THE FAA UPON ARR. I TALKED TO THE AREA MGR. HE INFORMED ME THAT A CLRNC WAS ISSUED TO ANOTHER FLT TO TURN TO A HDG; DSND TO AN ALT AND CHANGE TO ANOTHER FREQ. HE ALSO SAID THAT MY FLT OBEYED THE COMMAND WITHOUT A CLRNC READBACK. HE SAID THAT HE WAS GOING TO FILE A LETTER OF PLTDEV. I KNOW THAT I DID READ BACK THE ATC INSTRUCTIONS. MY FO; WHO WAS FLYING EVEN HEARD ME. I FEEL VERY SURE THAT THE CLRNC WAS FOR MY FLT NUMBER. I WAS USING A BOOM MIKE AND EARPIECE THAT WAS JUST BACK FROM THE REPAIR STATION FOR THE SECOND TIME. A RAMP PERSON AND ZJX BOTH SAID THAT THE XMITTER WAS WEAK BUT READABLE. THE ACFT LOGBOOK HAD PREVIOUS WRITE-UP OF XMITTING PROBLEMS. ONE ON PAGE IT SAID 'CAPT'S MIKE ONLY XMITS INTERMITTENTLY 50 PERCENT OF THE TIME IT IS CARRIER ONLY' AND PAGE STATED 'BOTH TRANSCEIVERS WILL XMIT ON FREQ 129.02 TO 129.32 BUT WILL NOT RECEIVE DUE TO A LOUD BUZZING NOISE. OCCURRED ENTIRE FLT UNTIL AFTER LNDG.' ON THE SECOND LEG WITH THE SAME ACFT; I WROTE #2 COM IN THE LOGBOOK AS HAVING PERIODIC STATIC DIFFICULT TO UNDERSTAND ATC. ALSO; THE FO MISSED 3 CLRNCS FROM ATC. THE RADIO WAS THEN EXCHANGED WITH ACARS RADIO ON THE NEXT STOP AND THE ACARS WAS UNABLE TO RECEIVE ON THE NEXT LEG. ON THE LAST FLT BDL TO ORD; I WROTE IN THE LOGBOOK PAGE 'TRANSMISSIONS INTERMITTENT ON 5 SEPARATE OCCASIONS; WE XMITTED; BUT ATC DID NOT RECEIVE.' 'ON 2 OCCASIONS ATC XMITTED BUT FO SAID HE DID NOT HEAR ANYTHING.' I FEEL IF I DID DEVIATE FROM ATC INSTRUCTIONS IT WAS BECAUSE OF TRANSCEIVERS MALFUNCTION. I ALSO FEEL THIS PROBLEM COULD STOP IF ATC CONFIRMED THE ACFT READBACK.